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Analytic varieties with finite volume amoebas are algebraic

  • Farid Madani EMAIL logo und Mounir Nisse
Veröffentlicht/Copyright: 21. August 2013

Abstract

In this paper, we study the amoeba volume of a given k-dimensional generic analytic variety V of the complex algebraic torus (*)n. When n2k, we show that V is algebraic if and only if the volume of its amoeba is finite. Moreover, in this case, we establish a comparison theorem for the volume of the amoeba and the coamoeba. Examples and applications to the k-dimensional affine linear spaces are also given.

Funding source: Alexander von Humboldt Foundation

Funding source: Mathematisches Forschungsinstitut Oberwolfach

Award Identifier / Grant number: Oberwolfach Leibniz Fellows

Funding source: NSF MCS

Award Identifier / Grant number: DMS-0915245

The authors thank the referee for useful comments which resulted in a better presentation of the paper.

Received: 2012-7-9
Revised: 2013-6-28
Published Online: 2013-8-21
Published in Print: 2015-9-1

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